Re: Summation problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg56675] Re: [mg56621] Summation problem*From*: Devendra Kapadia <dkapadia at wolfram.com>*Date*: Tue, 3 May 2005 05:26:26 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On Sat, 30 Apr 2005, jaropis wrote: > Why can't Mathematica sum: > Sum[I^n/n,{n,1,Infinity}] > and gives the (incorrect) answer, that this is divergent while it can do: > Sum[I^(n+1)/n,{n,1,Infinity}] > correctly? > > Jaroslaw Piskorski > Hello Jaroslaw Piskorski, Thank you for reporting this problem with an infinite sum. This is caused by a failure to detect the conditional convergence of the sum in your first example, in Mathematica 5. A workaround for the problem is to replace 'I' by the symbolic quantity 'x' and then substitute 'x' with 'I', as shown below. ========================================================== In[1]:= $Version Out[1]= 5.1 for Linux (February 20, 2005) In[2]:= Sum[x^n/n,{n,1,Infinity}]/.{x-> I} Out[2]= -Log[1 - I] In[3]:= N[%] Out[3]= -0.346574 + 0.785398 I In[4]:= NSum[I^n/n,{n,1,Infinity}] Out[4]= -0.346574 + 0.785398 I ============================================================ Sorry for the inconvenience caused by this problem. Devendra Kapadia. Wolfram Research, Inc.

**Follow-Ups**:**Re: Re: Summation problem***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>